C J T If: $ CT = 100$, $ JT = 5x + 5$, and $ CJ = 6x + 7$, Find $JT$.
Solution: From the diagram, we can see that the total length of ${CT}$ is the sum of ${CJ}$ and ${JT}$ $ {CJ} + {JT} = {CT}$ Substitute in the expressions that were given for each length: $ {6x + 7} + {5x + 5} = {100}$ Combine like terms: $ 11x + 12 = {100}$ Subtract $12$ from both sides: $ 11x = 88$ Divide both sides by $11$ to find $x$ $ x = 8$ Substitute $8$ for $x$ in the expression that was given for $JT$ $ JT = 5({8}) + 5$ Simplify: $ {JT = 40 + 5}$ Simplify to find ${JT}$ : $ {JT = 45}$